CN111638641A - Design method of fractional order active disturbance rejection controller for regulating and controlling motor speed loop - Google Patents

Design method of fractional order active disturbance rejection controller for regulating and controlling motor speed loop Download PDF

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CN111638641A
CN111638641A CN202010469843.1A CN202010469843A CN111638641A CN 111638641 A CN111638641 A CN 111638641A CN 202010469843 A CN202010469843 A CN 202010469843A CN 111638641 A CN111638641 A CN 111638641A
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motor speed
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speed loop
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CN111638641B (en
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罗映
陈鹏冲
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Huazhong University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00—Automatic controllers
    • G05B11/01—Automatic controllers electric
    • G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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Abstract

The invention belongs to the technical field related to controller design and discloses a design method of a fractional order active disturbance rejection controller for regulating and controlling a motor speed loop. The method comprises the following steps: s1, establishing the relation between the motor speed loop and the fractional order active disturbance rejection controller, and establishing the control rate u of the motor speed loop system to be regulated and controlled and the output u of the fractional order PD controller0And a relational expression of total disturbance f in a motor speed loop system to be regulated; s2 designing an extended state observer; s3, a closed-loop control system comprising the extended state observer, the PD controller, the gain-phase margin tester and the compensated speed loop control object is constructed, unknown parameters in the extended state observer and the PD controller are solved, and therefore the design of the fractional order active disturbance rejection controller is achieved. The invention realizes the design of the controller, and has strong robustness and high precision.

Description

Design method of fractional order active disturbance rejection controller for regulating and controlling motor speed loop
Technical Field
The invention belongs to the technical field related to controller design, and particularly relates to a design method of a fractional order active disturbance rejection controller for regulating and controlling a motor speed loop.
Background
The permanent magnet synchronous motor is widely applied in various fields, most of various automation equipment and robots adopt the permanent magnet synchronous motor, the permanent magnet synchronous motor has the advantages of high response speed, high precision, high power and the like, and a speed ring is the most important ring in motor vector control, so that the precise control of the speed ring of the permanent magnet synchronous motor is very critical.
Currently, the most common speed loop controller is a PID, but its resistance to external disturbances is limited. The active disturbance rejection control method is proposed by professor kyoto, han scholars, and has been widely paid attention and applied in recent years. The fractional order controller is a general form of the integer order controller, and the control performance of the fractional order controller is proved to be superior to that of the integer order controller. Therefore, the present invention provides a fractional auto-disturbance-rejection controller. Regarding the setting method of the active disturbance rejection controller, the method based on the frequency domain index has not been taken into consideration, but the frequency domain method is important in engineering application, so the invention provides the parameter setting method of the active disturbance rejection controller based on the frequency domain index and the time domain index.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a design method of a fractional order active disturbance rejection controller for regulating and controlling a motor speed loop, wherein the design method of the fractional order active disturbance rejection controller is realized by adopting the fractional order active disturbance rejection controller to control the motor speed loop and adopting a gain-phase margin tester to solve the solution of unknown parameters in the fractional order active disturbance rejection controller.
To achieve the above object, according to the present invention, there is provided a design method of a fractional order active disturbance rejection controller for regulating a speed loop of a motor, the design method comprising the steps of:
s1 construction of relation between motor speed loop and fractional order active disturbance rejection controller
For a motor speed loop system to be regulated and controlled, a fractional order active disturbance rejection controller is adopted to regulate and control a speed loop of the motor speed loop system to be regulated and controlled, the fractional order active disturbance rejection controller comprises a fractional order PD controller and an extended state observer, and the control rate u of the motor speed loop system to be regulated and controlled and the output of the fractional order PD controller are constructedu0The relation formula (I) of the total disturbance f in the motor speed loop system to be regulated and controlled is shown, wherein the total disturbance f in the motor speed loop system to be regulated and controlled is estimated through the extended state observer;
s2 design extended state observer
For a motor speed loop system to be regulated and controlled, acquiring a differential equation and a state space model of a motor speed loop control object, and designing an extended state observer according to the effect of the extended state observer on estimating the total disturbance;
s3 solving unknown parameters in extended state observer and PD controller
S31, according to the relation (I), compensating the motor speed loop object to be regulated and controlled by the total disturbance estimated by the extended state observer, so as to obtain a compensated motor speed loop control object;
s32, constructing a closed-loop control system comprising an extended state observer, a PD controller, a gain-phase margin tester and a compensated speed loop control object;
s33, calculating unknown parameters in the extended state observer and the fractional order PD controller by using the constraint conditions and the boundary conditions of the closed-loop control system, and designing the fractional order active disturbance rejection controller.
Further preferably, in step S1, the relation (one) is performed according to the following expression:
Figure BDA0002513901400000021
where b is the motor speed loop gain.
Further preferably, in step S1, the transfer function of the fractional order PD controller is:
CFOPD(s)＝Kp+Kdsμ
wherein, CFOPD(s) is the transfer function of the fractional order PD controller, KpAnd KdAre unknown parameters, proportional gain and differential gain, respectively, μ is the order of differentiation, μ ∈ (0,2), s is lapraAnd (5) a gaussian operator.
Further preferably, in step S2, the model of the extended state observer is performed according to the following expression:
Figure BDA0002513901400000031
in the formula (I), the compound is shown in the specification,
Figure BDA0002513901400000032
C＝[1 0 0]
L＝[β1β2β3]Tis the gain of the extended state observer, β1，β2And β3Are all unknown parameters, z ═ z1z2z3]TWherein z is1，z2And z3Are all the outputs of the extended state observer, z1And z2For estimating the derivatives of y and y, respectively, z3And estimating the total disturbance f, A, B and C to be intermediate variables respectively, wherein u is the control rate of the motor speed loop system to be regulated and controlled, and y is the output of the motor speed loop system to be regulated and controlled.
Further preferably, in step S3, the compensated motor speed loop control objects are:
Figure BDA0002513901400000033
β1＝3ωo
β2＝3ωo 2
β3＝ωo 3
wherein, Pc(s) is the compensated motor speed loop control object, a is the motor speed loop model parameter, β1＝3ωo，β2＝3ωo 2And β3＝ωo 3，ωoIs the bandwidth of the extended state observer.
Further preferably, in step S32, the transfer function of the closed-loop control system is:
Figure BDA0002513901400000034
the characteristic equation of the transfer function is:
D(Kp,Kd,μ,A,φ；s)＝(s5+(a+β1)s4+(aβ1+β2)s3+(aβ2+β3)s2)+
Ae-jφ(Kp+Kdsμ)(s3+β1s2+β2s+β3)
where A is the amplitude margin, φ is the phase margin, and G(s) is the transfer function of the closed-loop control system.
Further preferably, in step S33, calculating the unknown parameters in the extended state observer and the PD controller using the constraints and boundary conditions of the closed-loop control system is performed according to the following steps:
s331, constructing constraint conditions of phase margin, crossing indexes and ITAE indexes;
s332 determining K according to the real root boundary, the infinite root boundary and the complex root boundarypAnd KdAnd KpAnd KdWith respect to μ and ω, respectivelyoThe relational expression of (1);
s333 in mu and omegaoWithin the range of [ mu ] and [ omega ] respectivelyoAssigning values of all mu and omega satisfying the above constraint conditions and boundary conditionsoForming a feasible solution set;
s334, carrying out simulation calculation on points in the feasible solution set to calculate ITAE values, and carrying out simulation calculation on mu and omega corresponding to the minimum value in the ITAE values obtainedoI.e. the desired value, mu and omega are usedoCalculating to obtain unknown parameters Kp、Kd、β1、β2And β3The value of (c).
Further preferably, in step S331, the phase margin, the crossing index and the ITAE index are performed according to the following expressions, respectively:
Figure BDA0002513901400000041
Figure BDA0002513901400000042
Figure BDA0002513901400000043
wherein, ω isgcIs the crossover frequency, dB is the unit of amplitude, t is the real-time simulation time, and e (t) is the error at time t.
Further preferably, in step S332, K ispAnd KdThe boundaries of (a) are:
Kp＝0，Kdno boundary exists;
Kpand KdWith respect to μ and ω, respectivelyoThe relationship of (A) is as follows:
Figure BDA0002513901400000051
Figure BDA0002513901400000052
wherein the content of the first and second substances,
Figure BDA0002513901400000053
F2E5is F2And E5Product between, F1F7Is F1And F7Product between, E6E7Is E6And E7Product between, E5E8Is E5And E8The product between them.
Generally, compared with the prior art, the technical scheme of the invention has the following beneficial effects:
1. the invention provides a fractional order active disturbance rejection controller applied to the speed control of a permanent magnet synchronous motor, which can realize the accurate control of the motor speed, and simultaneously considers the frequency domain and time domain indexes, so that the control system has strong robustness and optimal dynamic control performance;
2. the invention adopts the frequency domain index phase margin and the crossing frequency for constructing the control system, so that the control system can meet the frequency domain index given by a user, and the dynamic performance of the control system is optimal by constructing the time domain constraint index of the control system.
Drawings
Fig. 1 is a schematic structural diagram of a motor speed loop system to be regulated and controlled connected with a fractional order active disturbance rejection controller according to a preferred embodiment of the present invention;
FIG. 2 is a schematic block diagram of a closed loop control system constructed in accordance with a preferred embodiment of the present invention;
FIG. 3 is a depiction of a stable region and an unstable region in accordance with a preferred embodiment of the present invention;
FIG. 4 is a diagram of controller parameters that meet a given frequency domain criterion, constructed in accordance with a preferred embodiment of the present invention;
FIG. 5 is a graphical three-dimensional visualization of controller parameters meeting a given frequency domain metric constructed in accordance with a preferred embodiment of the present invention;
FIG. 6 is a J constructed in accordance with a preferred embodiment of the present inventionITAEAnd μ;
FIG. 7 is a diagram of all controller parameters that satisfy the frequency domain criterion constructed in accordance with the preferred embodiment of the present invention:
FIG. 8 is a simulation calculated J for all controller parameters constructed in accordance with a preferred embodiment of the present inventionITAE。
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
S1 construction of relation between motor speed loop and fractional order active disturbance rejection controller
For a motor speed loop system to be regulated and controlled, a fractional order active disturbance rejection controller is adopted to regulate and control a speed loop of the motor speed loop system to be regulated and controlled, the fractional order active disturbance rejection controller comprises a fractional order PD controller and an extended state observer, as shown in FIG. 1, the right side in the figure is the motor speed loop system to be regulated and controlled, the left side is the fractional order active disturbance rejection controller, and the fractional order active disturbance rejection controller is used for regulating and controlling the speed loop of the motor speed loop system to be regulated and controlled;
reference input u for constructing motor speed loop system to be regulated and output u of fractional order PD controller0And a relational expression (I) of the total disturbance f in the motor speed loop system to be regulated, wherein the total disturbance f in the motor speed loop system to be regulated is estimated by an extended state observer, and the relational expression (I) is as follows:
Figure BDA0002513901400000061
s2 design extended state observer
(1) Extended state observer
The motor speed loop control objects are as follows:
Figure BDA0002513901400000071
the structure of the fractional order active disturbance rejection controller consists of a fractional order PD controller and an ESO, wherein the ESO is an extended state observer;
the motor speed control object can be written as:
Figure BDA0002513901400000072
wherein y is the system output, u is the reference input, d is the external disturbance, f is the total disturbance, and the total disturbance comprises the model unknown dynamics and the external disturbance.
ESO is used to estimate the total disturbance f, defined assuming f is guided
Figure BDA0002513901400000073
The state space model of equation (1) is:
Figure BDA0002513901400000074
wherein
Figure BDA0002513901400000075
According to the above formula, the ESO can be designed as:
Figure BDA0002513901400000076
wherein L is [ β ]1β2β3]TIs the gain of ESO, z ═ z1z2z3]T,z1,z2,z3Is the output of the ESO: z is a radical of1,z2Estimating y and its derivative, z, respectively3Estimating a total disturbance f, the total disturbance being compensated by:
Figure BDA0002513901400000077
wherein u is0Is the output of the fractional order PD controller.
(2) Fractional order PD controller
The transfer function of the fractional order PD controller is:
CFOPD＝Kp+Kdsμ(6)
wherein, KpAnd KdIs the proportional and derivative gain, μ is the derivative order, μ ∈ (0,2)
S3 solving unknown parameters in extended state observer and PD controller
S31 performs laplace transform on equation (4) to solve the equation set:
Figure BDA0002513901400000081
according to the formulas (1), (5) and (7), the speed loop control object after disturbance compensation is obtained as follows:
Figure BDA0002513901400000082
wherein the content of the first and second substances,
β1＝3ωo,β2＝3ωo 2,β3＝ωo 3(9)
s32, constructing a closed-loop control system comprising an extended state observer, a PD controller, a gain-phase margin tester and a compensated speed loop control object;
as shown in fig. 2, in which M isTRepresenting a gain-phase margin tester, DFOPD(s) stands for PD controller, PcAnd(s) represents a compensated speed loop control object, and the three are connected in sequence to form a closed-loop control system.
S33 calculates the unknown parameters in the extended state observer and the PD controller using the constraint conditions and the boundary conditions of the closed-loop control system as follows:
(1) constraint conditions
In the invention, two frequency domain indexes and one time domain index are used for designing the fractional order active disturbance rejection controller. The two frequency domain indicators are:
phase margin:
Figure BDA0002513901400000083
the crossing frequency:
Figure BDA0002513901400000084
the time domain index is:
ITAE index
Figure BDA0002513901400000091
(2) Boundary condition
MT is a Gain-Phase Margin Tester, which can provide boundary information of a stable region, and has a transfer function of:
MT(A,φ)＝Ae-jφ(10)
the transfer function of the closed-loop control system is as follows:
Figure BDA0002513901400000092
the closed loop transfer function has the following characteristic equation:
Figure BDA0002513901400000093
determining the parameter boundary specifically as follows:
range of: for the order μ of a fractional order PD controller, its range is defined as μ e (0, 2);
② solid root boundary is defined as D (K)p,Kdμ, A, φ; s-0) 0, hence KpThe boundaries of (a) are:
Kp＝0 (13)
③ infinite root boundary since the f relative order between the numerator and denominator of control object equation (8) is 2, KdNo boundary exists;
④ multiple root boundary s ═ j ω is substituted into (10), and the multiple root boundary can be defined as D (K)p,Kdμ, A, φ; s ═ j ω) ═ 0, i.e.
Figure BDA0002513901400000094
The real and imaginary parts of the above equation are each equal to 0, i.e.
F1+A(KpE5+KdE6)＝0,
F2+A(KpE7+KdE8)＝0
Wherein the content of the first and second substances,
F1＝(a+β1)ω4-(aβ2+β3)ω2,F2＝ω5-(aβ1+β2)ω3,
E3＝-ω3+β2ω,E4＝-β1ω2+β3,E5＝E4cosφ+E3sinφ,
Figure BDA0002513901400000101
E7＝E3cosφ+E4sinφ,
Figure BDA0002513901400000102
solving the equation yields, from the above equation:
Figure BDA0002513901400000103
thus, given a 1, 0, fixed μ, ωoPlane of parameters (K)p,Kd) The device is divided into a stable region and an unstable region by a solid root boundary and a multiple root boundary.
And the fractional order active disturbance rejection controller meets the frequency domain index:
the characteristic equation of the closed loop transfer function (11) is:
1+MT(A,φ)CFOPD(s)Pc(s)|s＝jω＝0
meaning that the open loop transfer function t(s) is equal to-1,
T(s)s＝jω＝MT(A,φ)CFOPD(s)Pc(s)|s＝jω＝-1
thus, it is possible to obtain an amplitude and phase of:
|MT(A,φ)CFOPD(s)Pc(s)|s＝jω＝1,
arg[MT(A,φ)CFOPD(s)Pc(s)]s＝jω＝-π
therefore, given a 1, all ω satisfying equation (14) can be considered to be the crossover frequency of the control system.
(3) Solving for unknown parameters
For practical application scenarios, the crossing frequency omega required to be satisfied is givengcAnd a phase margin phimFix mu, omegaoOther two parameters K of fractional order auto-disturbance rejection controllerpAnd KdCan be determined as a point of the parameter plane, and then scanning all μ ∈ (0,2), a curve can be obtained in the three-dimensional parameter space, where all points satisfy ωgcAnd phim。
Then all omega are scannedo∈(ωgc,ωmax)(ωoThe larger the disturbance, the stronger the ability to estimate the disturbance, but at the same time the noise will be amplified, therefore ω ismaxShould be valued according to the actual environment), K can be obtainedp、KdMu three-dimensional graph, the controller parameter corresponding to each point on the graph satisfies the crossing frequency omegagcAnd a phase margin phimThe points obtained above are simulated, ITAE is calculated, and omega can be obtainedo,μ,JITAESelecting the smallest JITAECorresponding μ and ωoUsing mu and omegaoCalculating to obtain unknown parameters Kp、Kd、β1、β2And β3To determine the unknown parameters in the fractional order PD controller and the extended state observer, i.e. to complete the design of the controller.
The simulation procedure is to calculate ITAE by the following formula,
Figure BDA0002513901400000111
where T is the simulation time and Δ T is the discrete time.
The present invention will be further illustrated with reference to specific examples.
1) Setting specific parameters of motor speed loop26.08 for a and 383.635 for b, the designed control system satisfies the crossing frequency of ωgc50rad/s, phase margin phim＝80°；
2) Select fractional order μ ═ 0.9 and ωoLet a be 1 and phi be 0 °, real root boundaries and complex root boundaries are drawn according to equations (13) and (15), and as shown in fig. 3, points are randomly selected and subjected to a simulation test to obtain a stable region and an unstable region. Let omega become omegagc＝50,φ＝φm80 °, according to (15), the controller parameter may be determined as "× a";
3) scanning all λ ∈ (0,2) to get a series of ". about." as shown in FIG. 4, showing it in three-dimensional space as shown in FIG. 5, all points in the figure satisfy the given crossover frequency and phase marginITAEMu and JITAEThe corresponding diagram is shown in fig. 6;
4) scanning all omegao∈(ωgc,ωmax) (in the motor control system herein, ω ismax800), all parameters satisfying a given frequency domain criterion can be obtained and visualized in the three-dimensional graph 7, all parameters simulating the calculated JITAEAs shown in FIG. 8, the smallest J is selectedITAEThe corresponding controller parameter is the designed fractional order active disturbance rejection controller.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (9)

1. A design method of a fractional order active disturbance rejection controller for regulating and controlling a motor speed ring is characterized by comprising the following steps:
s1 construction of relation between motor speed loop and fractional order active disturbance rejection controller
For a motor speed loop system to be regulated and controlled, a fractional order active disturbance rejection controller is adopted to regulate and control a speed loop of the motor, and the fractional order active disturbance rejection controllerThe device comprises a fractional order PD controller and an extended state observer, and the control rate u of a motor speed loop system to be regulated and controlled and the output u of the fractional order PD controller are constructed0The relation formula (I) of the total disturbance f in the motor speed loop system to be regulated and controlled is shown, wherein the total disturbance f in the motor speed loop system to be regulated and controlled is estimated through the extended state observer;
s2 design extended state observer
For a motor speed loop system to be regulated and controlled, acquiring a differential equation and a state space model of a motor speed loop control object, and designing an extended state observer according to the effect of the extended state observer on estimating the total disturbance;
s3 solving unknown parameters in extended state observer and PD controller
S31, according to the relation (I), compensating the motor speed loop object to be regulated and controlled by the total disturbance estimated by the extended state observer, so as to obtain a compensated motor speed loop control object;
s32, constructing a closed-loop control system comprising an extended state observer, a PD controller, a gain-phase margin tester and a compensated speed loop control object;
s33, calculating unknown parameters in the extended state observer and the fractional order PD controller by using the constraint conditions and the boundary conditions of the closed-loop control system, and designing the fractional order active disturbance rejection controller.
2. The method of claim 1, wherein in step S1, the relation (one) is expressed by the following expression:
Figure FDA0002513901390000021
where b is the motor speed loop gain.
3. The method as claimed in claim 1, wherein in step S1, the transfer function of the fractional order PD controller is:
CFOPD(s)＝Kp+Kdsμ
wherein, CFOPD(s) is the transfer function of the fractional order PD controller, KpAnd KdAre unknown parameters, proportional gain and differential gain, respectively, μ is the order of differentiation, μ ∈ (0,2), and s is the laplacian.
4. The method of claim 1, wherein in step S2, the model of the extended state observer is expressed by the following expression:
Figure FDA0002513901390000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002513901390000023
C＝[1 0 0]
L＝[β1β2β3]Tis the gain of the extended state observer, β1，β2And β3Are all unknown parameters, z ═ z1z2z3]TWherein z is1，z2And z3Are all the outputs of the extended state observer, z1And z2For estimating the derivatives of y and y, respectively, z3And estimating the total disturbance f, A, B and C to be intermediate variables respectively, wherein u is the control rate of the motor speed loop system to be regulated and controlled, and y is the output of the motor speed loop system to be regulated and controlled.
5. The method as claimed in claim 1, wherein in step S3, the compensated motor speed loop control objects are:
Figure FDA0002513901390000024
β1＝3ωo
β2＝3ωo 2
β3＝ωo 3
wherein, Pc(s) is the compensated motor speed loop control object, a is the motor speed loop model parameter, β1＝3ωo，β2＝3ωo 2And β3＝ωo 3，ωoIs the bandwidth of the extended state observer.
6. The method of claim 5, wherein in step S32, the transfer function of the closed-loop control system is:
Figure FDA0002513901390000031
the characteristic equation of the transfer function is:
D(Kp,Kd,μ,A,φ；s)＝(s5+(a+β1)s4+(aβ1+β2)s3+(aβ2+β3)s2)+Ae-jφ(Kp+Kdsμ)(s3+β1s2+β2s+β3)
where A is the amplitude margin, φ is the phase margin, and G(s) is the transfer function of the closed-loop control system.
7. The method of claim 6, wherein the step of calculating the unknown parameters in the extended state observer and the PD controller by using the constraints and boundary conditions of the closed-loop control system in the step S33 is performed according to the following steps:
s331, constructing constraint conditions of phase margin, crossing indexes and ITAE indexes;
s332 determining K according to the real root boundary, the infinite root boundary and the complex root boundarypAnd KdAnd KpAnd KdWith respect to μ and ω, respectivelyoThe relational expression of (1);
s333 in mu and omegaoWithin the range of [ mu ] and [ omega ] respectivelyoAssigning values of all mu and omega satisfying the above constraint conditions and boundary conditionsoForming a feasible solution set;
s334, carrying out simulation calculation on points in the feasible solution set to calculate ITAE values, and carrying out simulation calculation on mu and omega corresponding to the minimum value in the ITAE values obtainedoI.e. the desired value, mu and omega are usedoCalculating to obtain unknown parameters Kp、Kd、β1、β2And β3The value of (c).
8. The method as claimed in claim 7, wherein in step S331, the phase margin, the crossing index and the ITAE index are respectively expressed as follows:
Figure FDA0002513901390000041
Figure FDA0002513901390000042
Figure FDA0002513901390000043
wherein, ω isgcIs the crossover frequency, dB is the unit of amplitude, t is the real-time simulation time, and e (t) is the error at time t.
9. The method of claim 7, wherein in step S332, K is the integer multiple of KpAnd KdThe boundaries of (a) are:
Kp＝0，Kdno boundary exists;
Kpand KdWith respect to μ and ω, respectivelyoThe relationship of (A) is as follows:
Figure FDA0002513901390000044
Figure FDA0002513901390000045
wherein the content of the first and second substances,
Figure FDA0002513901390000046
F2E5is F2And E5Product between, F1F7Is F1And F7Product between, E6E7Is E6And E7Product between, E5E8Is E5And E8The product between them.
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